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Practice problems: 1. Factor $x^3 + 3x^2y + 3xy^2 + y^3$. 2. Simplify $(x^3 - 8)/(x - 2)$. 3. Expand $(x^2 + 1)(x - 5)(2x + 3)$. 4. Solve $\sin x = 2 - x$ for $x$. 5. Solve $5x + 2y + 4z = 8$, $-3x + y + 2z = -7$, $2x + y + z = 3$ for $x$, $y$ and $z$. 6. Solve $y^2 - 5xy - y + 6x^2 + x = 2$ for $x$. 7. Find the first derivative of the function $(\sin x)/(\ln(x^2 + 1)) - e^x$ and evaluate it at $x = 3$. 8. Find the 12th derivative of the function $(x/2 + 1)^{65}$ 9. Find the first and second partial derivatives of the function $e^{x^2} \sin xy$

          Practice problems:
1. Factor $x^3 + 3x^2y + 3xy^2 + y^3$.
2. Simplify $(x^3 - 8)/(x - 2)$.
3. Expand $(x^2 + 1)(x - 5)(2x + 3)$.
4. Solve $\sin x = 2 - x$ for $x$.
5. Solve $5x + 2y + 4z = 8$, $-3x + y + 2z = -7$, $2x + y + z = 3$ for $x$, $y$ and $z$.
6. Solve $y^2 - 5xy - y + 6x^2 + x = 2$ for $x$.
7. Find the first derivative of the function $(\sin x)/(\ln(x^2 + 1)) - e^x$ and evaluate it at $x = 3$.
8. Find the 12th derivative of the function $(x/2 + 1)^{65}$
9. Find the first and second partial derivatives of the function $e^{x^2} \sin xy$

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Practice problems:
1. Factor x^3 + 3x^2y + 3xy^2 + y^3.
2. Simplify (x^3 - 8)/(x - 2).
3. Expand (x^2 + 1)(x - 5)(2x + 3).
4. Solve sin x = 2 - x for x.
5. Solve 5x + 2y + 4z = 8, -3x + y + 2z = -7, 2x + y + z = 3 for x, y and z.
6. Solve y^2 - 5xy - y + 6x^2 + x = 2 for x.
7. Find the first derivative of the function (sin x)/(ln(x^2 + 1)) - e^x and evaluate it at x = 3.
8. Find the 12th derivative of the function (x/2 + 1)^65
9. Find the first and second partial derivatives of the function e^x^2sin xy

Added by Kristy A.

Computer Science and Information Technology

Trishna Knowledge Systems 2018 Edition

Instant Answer

Solved by Expert Vandit Tyagi

Step 1

To factor x+3xy+3xy+y^3, we can group the terms: x + 3xy + 3xy + y^3 = (x + 3xy) + (3xy + y^3) Now, we can factor out common terms from each group: (x + 3xy) + (3xy + y^3) = x(1 + 3y) + y^3(3 + y) So, the factored form is x(1 + 3y) + y^3(3 + y). Show more…

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I need a solution within 15 minutes. Practice problems: 1. Factor x+3xy+3xy+y^3 2. Simplify x^3-8/x-2. 3. Expand x+1/x-5*2x+3 4. Solve sinx=2-x for x. Matlab 5. Solve 5x+2y+4z=8, -3x+y+2z=-7, 2x+y+z=3 for x, y, and z. 6. Solve y^2-5xy-y+6x^2+x=2 for x. 7. Find the first derivative of the function (sinx/Inx+1)-e and evaluate it at x=3. 8. Find the 12th derivative of the function x/2+1. 9. Find the first and second partial derivatives of the function esinry.

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